Questions: Gravity Waves and Wind-Driven Ocean Surface Waves

Question 1

A surfer in California is riding waves generated by a storm near New Zealand. A student says 'the water from the New Zealand storm traveled all the way to California.' What is wrong with this claim?

• A. Water cannot travel between hemispheres because of the equator barrier
• B. Individual water particles trace circular orbits and return nearly to their starting position after each wave cycle — the wave transmits energy, not water
• C. The student is partially right: surface water travels, but deep water does not
• D. The student is correct: waves are by definition moving water

Answer: (B)

This is the central misconception about ocean waves. The wave is not a column of water moving forward — it is a pattern of energy moving through water. Individual water particles execute circular orbits, advancing slightly forward and then returning as each wave crest passes. A beach ball floating on the surface bobs up and down and slightly forward-and-back, but it does not ride the wave to shore. What crosses the Pacific is the energy pattern, not the New Zealand water itself.

Question 2

Right after a major storm, a buoy near the storm records chaotic waves of many different heights and periods. Two weeks later, a buoy 5,000 km away records smooth, evenly-spaced swell. What explains this transformation?

• A. The storm's total energy dissipated during travel, leaving only weak, regular oscillations
• B. The ocean absorbed the irregular wave components preferentially, filtering out the choppiness
• C. Dispersion: longer-period waves travel faster and outrun shorter ones, so the wave spectrum sorts itself by period as it travels
• D. The distant buoy is in calmer water that dampened the irregular components

Answer: (C)

Dispersion is the key: in deep water, wave speed increases with wavelength (and period). Longer-period waves generated by the storm outrun the shorter ones, arriving at distant shores earlier and separately. By the time the wave spectrum has traveled thousands of kilometers, it has sorted itself — the fastest, longest-period waves arrive first, followed by progressively shorter ones. The result is organized swell rather than chaotic wind-sea. Energy is not lost; it is separated and sorted by wave speed.

Question 3

At a depth equal to about half the wavelength, the orbital motion of water particles becomes negligible — this is why deep-water waves do not interact with the seafloor.

• T. True
• F. False

Answer: True

Wave-induced orbital motion decreases exponentially with depth. At a depth of roughly half the wavelength (L/2), particle displacement is less than 4% of what it is at the surface — effectively negligible. This defines the deep-water limit: waves whose wavelength is short relative to water depth 'feel' no bottom and travel according to deep-water wave theory. When depth decreases below L/2, the wave begins to interact with the seafloor, slowing, steepening, and eventually breaking.

Question 4

Larger ocean waves generally travel faster than smaller ones.

• T. True
• F. False

Answer: False

In deep water, wave speed depends on wavelength (or equivalently, period) — not on wave height. A long-period swell of modest height travels faster than a high-amplitude short-period wave. This is dispersion: c = √(gλ/2π) for deep-water gravity waves, where λ is wavelength and g is gravitational acceleration. Wave height does not appear in this relationship. This is why swell from a distant storm sorts by period, not by how big the waves were.

Question 5

Why do swell waves that have traveled thousands of kilometers from their source tend to be cleaner and more regular than the chaotic waves near the generating storm? What physical process produces this?

Model answer: Dispersion sorts the wave spectrum during travel. In deep water, wave speed increases with wavelength and period (longer waves travel faster). Near the storm, waves of all periods are generated simultaneously, producing chaotic wind-sea. As this spectrum propagates outward, the faster long-period waves outrun the slower short-period waves. After thousands of kilometers of travel, the wave energy has sorted into distinct wave trains organized by period — long-period swell arrives first, followed by progressively shorter components. The result is clean, evenly-spaced swell rather than a confused sea.

This sorting is also why the wave period at a distant shore tells you something about the storm's timing: as a swell event progresses, the arriving period systematically decreases from very long to shorter, because the wave spectrum is being delivered in speed order. Experienced surfers and oceanographers use this pattern to infer storm distance and timing.